The same problem exists for other plotting methods (ListPlot3D, ListContourPlot, etc.). While rescaling the coordinates is a simple fix, is it possible to plot datasets of this sort without first rescaling the coordinates?

Now I don't know exactly how to fix this, but my guess is that the mesh function relies on the Delaunay triangulation of the set of points and somewhere in there, something is either dangerously close to machine precision or getting Chopped. Since the default tolerance for chopping is $10^{-10}$, it is plausible that this is what is happening.

Very interesting. Your point about the meshing seems to be correct. The mesh seems to converge to a stable sort of version with scaling here ~10^8.
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Eli LanseyApr 18 '12 at 2:26

@EliLansey Also, the mesh depends on the order the points in the original data, suggesting that it might be a naïve incremental triangulation. To see what I mean, try ListDensityPlot[RandomSample[data, 441] #, Mesh -> All, ImageSize -> 300] & /@ {1, 100, 10^3, 10^4}
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The Toad♦Apr 18 '12 at 2:39

if you add MaxPlotPoints -> 20 then last 2 graphs are fine... and MaxPlotPoints -> 10 then 3rd graph is fine but not 4th.
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s.s.oApr 18 '12 at 4:45

The ListDensityPlot works with Graphics options and primitives are converted to integer somewhere as you said it chops the data so does the ListPlot3D... And with graphics it has no option for accuracy like some other plots.
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s.s.oApr 18 '12 at 4:52

I think you mean DataRange -> {{-10^-7, 10^-7}, {-10^-7, 10^-7}}. This works because using Datarange makes ListDensityPlot completely ignore the x and y values.
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Sjoerd C. de VriesApr 17 '12 at 21:07

I didn't test if the ranges are correct. Just tried to give an example. But it was working. May be you are right. I'll check...
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s.s.oApr 17 '12 at 21:12

This doesn't work. This is helpful if you have an array of values like Table[x^2 + y^2, {x, -100, 100, 10}, {y, -100, 100, 10}], but here I have the x and y values given.
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Eli LanseyApr 17 '12 at 21:25

1

yep, both of you are right and same problem exist for ListPlot3D too. Some how it's related to precision 10^-5 works but not 10^-9...
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s.s.oApr 17 '12 at 21:35

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